To solve the inequality \( x - 5 < \frac{x}{6} \), we want to isolate \( x \) on one side.
Let's analyze the options provided:
A. This option involves dividing by 6, which complicates the left side without isolating \( x \).
B. This option recommends dividing by \( x \). However, we have to be cautious, as dividing by \( x \) can change the direction of the inequality depending on whether \( x \) is positive or negative, and it won't help in isolating \( x \).
C. This option suggests multiplying both sides by \( x \), which also is risky for the same reason as option B.
D. This option suggests multiplying both sides by 6, which is an effective way to eliminate the fraction and simplify the inequality.
Given these considerations, the best first step to solve the inequality \( x - 5 < \frac{x}{6} \) is option D:
Multiply both sides of the inequality by 6 to simplify: \( 6(x - 5) < x \) resulting in \( 6x - 30 < x \).
So, the correct answer is D.